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書籍 A, and the adjacent angular points of the squares joined, the sum of the squares... の書籍検索結果 37 件中 1 - 10 件目
" A, and the adjacent angular points of the squares joined, the sum of the squares of the three joining lines is equal to three times the sum of the squares of the sides of the triangle. "
A Sequel to the First Six Books of the Elements of Euclid: Containing an ... - 28 ページ
John Casey 著 - 1882 - 158 ページ
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - 1823 - 576 ページ
...the squares of the twelve edges, plus the sum of the squares of the twelve diagonals of tin- faces, is equal to three times the sum of the squares of the four diagonals which cross the solid, plus four times the sumof the squares of the six right lines...

A Collection of Cambridge Mathematical Examination Papers: Papers in the ...

John Martin Frederick Wright - 1831
...be joined ; the sum of the squares of the sides of the hexagonal figure thus formed is equal to four times the sum of the squares of the sides of the triangle. 14,. If all the angular points of a regular polygon of n sides be joined, and r be the radius of the circumscribing...

The Elements of Mechanics, Comprehending Statics and Dynamics: With a ...

John Radford Young - 1832 - 326 ページ
...+ BG2 + CG2) = AB2 + BC2 + CAt; that is, in any plane triangle the sum of the squares of the sides is equal to three times the sum of the squares of the distances of the Tertices from the centre of gravity of the triangle. If three equal bodies be placed...

A Treatise on Statics: Containing the Theory of the Equilibrium of Forces ...

Samuel Earnshaw - 1845 - 233 ページ
...147), EC- + AC? + AB* = 3. (AGP + BG* + CCP). Hence the sum of the squares of the sides of a triangle is equal to three times the sum of the squares of the distances of its angular points from its centre of gravity. 167- COR. 4. In the case of the triangular...

Mechanics for Practical Men

1845 - 238 ページ
...is at the point of intersection 52 The sum of the squares of the three sides of any plane triangle, is equal to three times the sum of the squares of the distances of its centre of gravity from the angular points 55 SECT. SIXTH. Of the centre of gravity...

Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...be joined ; the sum of the squares of the sides of the hexagonal figure thus formed is equal to four times the sum of the squares of the sides of the triangle. GEOMETRICAL EXERCISES ON BOOK III. THEOREM I. If AB, CD be chords of a circle at right angles to each...

Encyclopædia metropolitana; or, Universal dictionary of knowledge ..., 第 3 巻

Edward Smedley - 1845
...(» — 3 („,' + nf + r). That is, in any plane triangle, the sum of the squares of the three sides is equal to three times the sum of the squares of the three lines drawn from each of its angles to the centre of gravity. 120. To find the centre of gravity...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...joined, the sura of the squares of the sides of the hexagonal figure thus formed will be equal to four times the sum of the squares of the sides of the triangle. 46. If two points be taken in the diameter of a circle equally distant from the centre, the sum of...

Elements of Geometry: With Practical Applications ...

George Roberts Perkins - 1847 - 308 ページ
...squares of the lines drawn from the angles of a triangle to the middle points of the opposite sides, is equal to three times the sum of the squares of the sides. Equation [9] gives this THEOREM. Sixteen times thf sum of the products, taken two at a time,...

The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides - 1849 - 108 ページ
...drawn to the points of bisection of the opposite sides, four times the sum of the squares of these lines is equal to three times the sum of the squares of the sides of the triangle. 12. If from any point within a rectangle lines be drawn to the angular points, the sums of the squares...




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